Lattice Monte-Carlo simulations with magnetic fields do not suffer from the sign problems.
There have been lattice studies on the chiral and deconfinement transitions [1]}, [2]}, various condensates such as chiral condensates [3]}, [4]} and the Polyakov loops [5]}, the string tension [6]}, [7]}, [8]}, equations of state [9]}, and hadron spectra [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}.
The effective model descriptions for these quantities are not straightforward, and the attempts to reproduce the lattice data should improve our understanding of each model.
